There generally develops in an image the phenomenon called stairup, an artifact in the form of stair, which is disadvantageous for the purpose of diagnostics, if the number of pixels is not enough in a diagnostic imaging system such as X-ray CT or MRI for displaying images. Hence, stairup has recently been avoided, by employing a display system with a larger number of pixels and rendering the size of one pixel smaller, so as to improve image quality. When the resolution of a display device is thus improved to improve an image itself proportionally, however, the ratio S/N of the data may be lowered so that the noise in the image may be increased to deteriorate the image. In case of X-ray CT, the decrease in the ratio S/N can be compensated by the increase in exposure dose, which causes detrimental effects to human body. In case of MRI, its decrease can be compensated by prolonged data collecting time, leading to the extension of imaging time to give more stress to a subjective. There are additional problems, involving the requirement of image reconstruction time to transform collected data into image data, and the increase in the cost of a device in relation thereto. In other words, in terms of processing an identical quantity of information, simple improvement of the display resolution without enhancing the resolution of image itself involves a vast amount of calculation process, which is not economical. Therefore, without increasing the number of data items at image reconstruction, it is desirable to use interpolation process with relatively less calculation process, so as to enlarge the image after reconstruction to obtain a high-quality display image.
FIGS. 4A and 4B are diagrams representing the interpolation process in conventional embodiments, where FIG. 4A is a diagram showing the data matrices before interpolation and FIG. 4B is a diagram showing the data matrices after interpolation. In FIGS. 4A and 4B, the black spots are reconstructed image data items, while the white spots are interpolated data items generated from the image data items. In case that the image restructured in the data matrix of 256.times.256 is displayed on a display device having the pixel number of 512.times.512, for example, two-fold enlargement is carried out in such manner that interpolated data items by linear interpolation and the like are inserted among the reconstructed data items of FIG. 4A as is shown in FIG. 4B. However, the frequency characteristic feature of the data items produced by interpolation is deteriorated generally, which causes the problems of the blurring in image and the change in its texture. In order to reduce the deterioration, there may be suggested the use of a higher-degree interpolation function. In that case, the time required for calculating the interpolation gets longer. When the point f(X) (X.sub.0 &lt;X&lt;X1) is to be determined between f(X.sub.0)=f.sub.0 and f(X.sub.1)=f.sub.1, according to one-dimensional Lagrange's interpolation of 2 k degree from the (2k+1) data items, the following is calculated; ##EQU1## (L.sub.k (X): weighing function of 2 k degree; f.sub.-k, . . . , f.sub.k : data sequence) Hence, the number of the calculation process to carrying out the interpolation for a two-dimensional image consequently increases in proportion with the degree number of the interpolation formula (1).
In obtaining image data for a display device of a larger number of pixels by increasing the number of image data items after reconstruction by means of interpolation without increasing the number of data items at reconstruction as has been described above, there may be caused the image deterioration by conventional low-degree interpolation process. When employing a higher-degree interpolation in order to compensate such deterioration, there may develop problems, such as the increase in the number of calculation process involving the prolongation of the processing time, and the elevation of the cost of a device therefor which is imposed by the complexity of a circuit construction.